Grade 8Magical Mathematics[Interesting Approach]
If a to the power of x=b to the power of y=c to the power of z and b square=ac,then y is equals to
1 Answer
Arun
Dear student
Given ax = by = cz and b2 = ac
Let ax = by = cz = k
Consider, ax = k ⇒ a = k1/x
Similarly, we get b = k1/y and c = k1/z
Now consider, b2 = ac
⇒ (k1/y)2 = (k1/x)(k1/z)
⇒ k2/y = k1/x + 1/z
Comparing both the sides, we get
(2/y) = (1/x) + (1/z)
⇒ (2/y) = (x + z)/xz
∴ y = (2xz)/(x + z)
Let ax = by = cz = k
Consider, ax = k ⇒ a = k1/x
Similarly, we get b = k1/y and c = k1/z
Now consider, b2 = ac
⇒ (k1/y)2 = (k1/x)(k1/z)
⇒ k2/y = k1/x + 1/z
Comparing both the sides, we get
(2/y) = (1/x) + (1/z)
⇒ (2/y) = (x + z)/xz
∴ y = (2xz)/(x + z)
Regards
Arun (askIITians forum expert)
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